Lyapunov Schmidt Methods In Nonlinear Analysis And Applications
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Lyapunov Schmidt Methods In Nonlinear Analysis And Applications
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Author : Nikolay Sidorov
language : en
Publisher: Springer Science & Business Media
Release Date : 2002-10-31
Lyapunov Schmidt Methods In Nonlinear Analysis And Applications written by Nikolay Sidorov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-10-31 with Mathematics categories.
Recent theory and applications of the Lyapunov-Shmidt method are presented in this specialized volume of use to mathematicians, physicists, and engineers interested in nonlinear equations. The chapters describe the Lyapunov-Shmidt method and its use for obtaining branching solutions for nonlinear equations using iterative techniques, techniques for constructing regularizing equations, the use of power geometry methods, the theory of branching for interlaced equations, applications of ideas of symmetry in the theory of bifurcations, applications in differential operator equations, and applied problems of mathematical physics. The four authors are Russian mathematicians who teach at the Irkutsk State U and the Ulyanovsk State Technical U. in Russia and the National U. of Colombia in Bogota. Annotation (c)2003 Book News, Inc., Portland, OR (booknews.com).
Lyapunov Schmidt Methods In Nonlinear Analysis And Applications
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Author : Nikolay Sidorov
language : en
Publisher:
Release Date : 2014-01-15
Lyapunov Schmidt Methods In Nonlinear Analysis And Applications written by Nikolay Sidorov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Lyapunov Schmidt Methods In Nonlinear Analysis And Applications
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Author : Nikolay Sidorov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Lyapunov Schmidt Methods In Nonlinear Analysis And Applications written by Nikolay Sidorov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
This book concentrates on the branching solutions of nonlinear operator equations and the theory of degenerate operator-differential equations especially applicable to algorithmic analysis and nonlinear PDE's in mechanics and mathematical physics. The authors expound the recent result on the generalized eigen-value problem, the perturbation method, Schmidt's pseudo-inversion for regularization of linear and nonlinear problems in the branching theory and group methods in bifurcation theory. The book covers regular iterative methods in a neighborhood of branch points and the theory of differential-operator equations with a non-invertible operator in the main expression is constructed. Various recent results on theorems of existence are given including asymptotic, approximate and group methods.
Methods In Nonlinear Analysis
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Author : Kung-Ching Chang
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-11-21
Methods In Nonlinear Analysis written by Kung-Ching Chang and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-11-21 with Mathematics categories.
Nonlinear analysis has developed rapidly in the last three decades. Theories, techniques and results in many different branches of mathematics have been combined in solving nonlinear problems. This book collects and reorganizes up-to-date materials scattered throughout the literature from the methodology point of view, and presents them in a systematic way. It contains the basic theories and methods with many interesting problems in partial and ordinary differential equations, differential geometry and mathematical physics as applications, and provides the necessary preparation for almost all important aspects in contemporary studies. There are five chapters that cover linearization, fixed-point theorems based on compactness and convexity, topological degree theory, minimization and topological variational methods. Each chapter combines abstract, classical and applied analysis. Particular topics included are bifurcation, perturbation, gluing technique, transversality, Nash–Moser technique, Ky Fan's inequality and equilibrium in game theory, setvalued mappings and differential equations with discontinuous nonlinear terms, multiple solutions in partial differential equations, direct method, quasiconvexity and relaxation, Young measure, compensation compactness method and Hardy space, concentration compactness and best constants, Ekeland variational principle, infinite-dimensional Morse theory, minimax method, index theory with group action, and Conley index theory. All methods are illustrated by carefully chosen examples from mechanics, physics, engineering and geometry. The book aims to find a balance between theory and applications and will contribute to filling the gap between texts that either only study the abstract theory, or focus on some special equations.
Methods Of Nonlinear Analysis
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Author : Pavel Drabek
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-10-24
Methods Of Nonlinear Analysis written by Pavel Drabek and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-10-24 with Mathematics categories.
In this book, the basic methods of nonlinear analysis are emphasized and illustrated in simple examples. Every considered method is motivated, explained in a general form but in the simplest possible abstract framework. Its applications are shown, particularly to boundary value problems for elementary ordinary or partial differential equations. The text is organized in two levels: a self-contained basic and, organized in appendices, an advanced level for the more experienced reader. Exercises are an organic part of the exposition and accompany the reader throughout the book.
Mathematics Of Complexity And Dynamical Systems
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Author : Robert A. Meyers
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-10-05
Mathematics Of Complexity And Dynamical Systems written by Robert A. Meyers and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-05 with Mathematics categories.
Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.
Approximation And Regularisation Methods For Operator Functional Equations
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Author : Nikolay Sidorov
language : en
Publisher: World Scientific
Release Date : 2025-03-05
Approximation And Regularisation Methods For Operator Functional Equations written by Nikolay Sidorov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-05 with Mathematics categories.
This book presents an overview of the most recent research and findings in the field of approximation and regularisation methods for operator-functional equations, and explores their applications in electrical and power engineering. It presents the state of the art in building operator theory, regularised numerical methods, and the verification of mathematical models for dynamical models based on integral and differential equations. Special attention is paid to Volterra models, a powerful tool for modelling hereditary dynamics.This book begins by exploring the solvability of singular integral equations and moves on to study approximation methods for linear operator equations and nonlinear integral equations. Following this, it examines loaded equations and bifurcation analysis, before concluding with an investigation of the applications of the contents of the book in electrical engineering and automation. Each chapter provides an overview and analysis of the relevant problem statements, outlines current methods within the field, and identifies future directions for research.With an interdisciplinary approach, this book is essential reading for anyone interested in operator-functional equations. Graduate students and professors in the fields of applied mathematics, physics, materials science, and numerical analysis will find this work insightful and valuable, as will industry professionals in related fields.
Linear And Nonlinear Functional Analysis With Applications Second Edition
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Author : Philippe G. Ciarlet
language : en
Publisher: SIAM
Release Date : 2025-04-23
Linear And Nonlinear Functional Analysis With Applications Second Edition written by Philippe G. Ciarlet and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-04-23 with Mathematics categories.
This new, considerably expanded edition covers the fundamentals of linear and nonlinear functional analysis, including distribution theory, harmonic analysis, differential geometry, calculus of variations, and degree theory. Numerous applications are included, especially to linear and nonlinear partial differential equations and to numerical analysis. All the basic theorems are provided with complete and detailed proofs. The author has added more than 450 pages of new material; added more than 210 problems; the solutions to all of the problems will be made available on an accompanying website; added two entirely new chapters, one on locally convex spaces and distribution theory and the other on the Fourier transform and Calderón–Zygmund singular integral operators; and enlarged and split the chapter on the “great theorems” of nonlinear functional analysis into two chapters, one on the calculus of variations and the other on Brouwer’s theorem, Brouwer’s degree, and Leray–Schauder’s degree. Ideal for both teaching and self-study, Linear and Nonlinear Functional Analysis with Applications, Second Edition is intended for advanced undergraduate and graduate students in mathematics, university professors, and researchers. It is also an ideal basis for several courses on linear or nonlinear functional analysis.
Bifurcation And Chaos Analysis Algorithms Applications
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Author : KÜPPER
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Bifurcation And Chaos Analysis Algorithms Applications written by KÜPPER and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This volume contains the proceedings of a conference held in Wiirzburg, August 20-24, 1990. The theme of the conference was Bifurcation and Chaos: Analysis, Algorithms, Ap plications. More than 100 scientists from 21 countries presented 80 contributions. Many of the results of the conference are described in the 49 refereed papers that follow. The conference was sponsored by the Deutsche Forschungsgemeinschaft, and by the Deutscher Akademischer Austauschdienst. We gratefully acknowledge the support from these agen cies. The science of nonlinear phenomena is evolving rapidly. Over the last 10 years, the emphasis has been gradually shifting. How trends vary may be seen by comparing these proceedings with previous ones, in particular with the conference held in Dortmund 1986 (proceedings published in ISNM 79). Concerning the range of phenomena, chaos has joined the bifurcation scenarios. As expected, the acceptance of chaos is less emotional among professionals, than it has been in some popular publications. A nalytical methods appear to have reached a state in which basic results of singularities, symmetry groups, or normal forms are everyday experience rather than exciting news. Similarly, numerical algorithms for frequent situations are now well established. Implemented in several packages, such algorithms have become standard means for attacking nonlinear problems. The sophisti cation that analytical and numerical methods have reached supports the vigorous trend to more and more applications. Pioneering equations as those named after Duffing, Van der Pol, or Lorenz, are no longer exclusively the state of art.
Concentration Analysis And Applications To Pde
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Author : Adimurthi
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-22
Concentration Analysis And Applications To Pde written by Adimurthi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-22 with Mathematics categories.
Concentration analysis provides, in settings without a priori available compactness, a manageable structural description for the functional sequences intended to approximate solutions of partial differential equations. Since the introduction of concentration compactness in the 1980s, concentration analysis today is formalized on the functional-analytic level as well as in terms of wavelets, extends to a wide range of spaces, involves much larger class of invariances than the original Euclidean rescalings and has a broad scope of applications to PDE. This book represents current research in concentration and blow-up phenomena from various perspectives, with a variety of applications to elliptic and evolution PDEs, as well as a systematic functional-analytic background for concentration phenomena, presented by profile decompositions based on wavelet theory and cocompact imbeddings.